Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 9.2, Problem 49PS
To determine
To find:Whether the
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2.
a. In each part express the vector as a linear combination of
2+x+4x², p₂ = 1 − x + 3x², and p3 = 3 + 2x + 5x².
pi
i. -9-7x - 15x²
ii. 6+11x + 6x²
=
iii. O
iv. 7 + 8x + 9x²
b. Suppose that vi
=
= (2, 1, 0, 3), v₂ = (3, −1, 5, 2), and №3 = (–1, 0, 2, 1).
Which of the following vectors are in span {1, 2, 3}?
i.
(2, 3, -7,3)
ii.
(0,0,0,0)
iii. (1,1,1,1)
iv. (-4, 6, -13, 4)
Solve the following exercises, you will need to show all your work to receive full credit. Consider the
matrix,
2 1 -2
2 3 -4
1
1
1
-
Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following:
1. find a basis of eigenvectors;
2. Find P such that P- AP is a diagonal matrix D. Give D
1. Write the vector
H-
16
as a linear combination of the vectors
and
D
Chapter 9 Solutions
Calculus
Ch. 9.1 - Prob. 1PSCh. 9.1 - Prob. 2PSCh. 9.1 - Prob. 3PSCh. 9.1 - Prob. 4PSCh. 9.1 - Prob. 5PSCh. 9.1 - Prob. 6PSCh. 9.1 - Prob. 7PSCh. 9.1 - Prob. 8PSCh. 9.1 - Prob. 9PSCh. 9.1 - Prob. 10PS
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Prob. 58PSCh. 9.7 - Prob. 59PSCh. 9.7 - Prob. 60PSCh. 9 - Prob. 1PECh. 9 - Prob. 2PECh. 9 - Prob. 3PECh. 9 - Prob. 4PECh. 9 - Prob. 5PECh. 9 - Prob. 6PECh. 9 - Prob. 7PECh. 9 - Prob. 8PECh. 9 - Prob. 9PECh. 9 - Prob. 10PECh. 9 - Prob. 11PECh. 9 - Prob. 12PECh. 9 - Prob. 13PECh. 9 - Prob. 14PECh. 9 - Prob. 15PECh. 9 - Prob. 16PECh. 9 - Prob. 17PECh. 9 - Prob. 18PECh. 9 - Prob. 19PECh. 9 - Prob. 20PECh. 9 - Prob. 21PECh. 9 - Prob. 22PECh. 9 - Prob. 23PECh. 9 - Prob. 24PECh. 9 - Prob. 25PECh. 9 - Prob. 26PECh. 9 - Prob. 27PECh. 9 - Prob. 28PECh. 9 - Prob. 29PECh. 9 - Prob. 30PECh. 9 - Prob. 1SPCh. 9 - Prob. 2SPCh. 9 - Prob. 3SPCh. 9 - Prob. 4SPCh. 9 - Prob. 5SPCh. 9 - Prob. 6SPCh. 9 - Prob. 7SPCh. 9 - Prob. 8SPCh. 9 - Prob. 9SPCh. 9 - Prob. 10SPCh. 9 - Prob. 11SPCh. 9 - Prob. 12SPCh. 9 - Prob. 13SPCh. 9 - Prob. 14SPCh. 9 - Prob. 15SPCh. 9 - Prob. 16SPCh. 9 - Prob. 17SPCh. 9 - Prob. 18SPCh. 9 - Prob. 19SPCh. 9 - Prob. 20SPCh. 9 - Prob. 21SPCh. 9 - Prob. 22SPCh. 9 - Prob. 23SPCh. 9 - Prob. 24SPCh. 9 - 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- 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .arrow_forwardDetermine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)arrow_forward7. Show that the vectors A=4a, -2a, +2a, and B = -6ā, +3ā, -3ā, are parallel to each other.arrow_forward
- 6. Write DÉ as a linear combination of the vectors i and j a) D (9,-6) E (-7, 2) first write in component form, then write as linear combination b) D (-3, 5.7) E (6,-8.1) 10+arrow_forward1.The following problems will all make reference to these three vectors: 4 7 A= 4 B = 5 C= -1 -4 -5 a. Calculate the following dot products: Ä•B, Ã•Č¸ and B•(À+2č). b. Which vector (among A, B, and C) is the longest? Which is the shortest? C. Calculate the vector product Â×(B×ċ).arrow_forwardWhich of the following vectors is a particular solution to the equation? Vị -4 -3 -9 -2 51 V2 -6 -6 -6 12 48 V3 -2 -10 60 127 V4 -7 -1 11 А. + c1 -1 1 -1 -2 -15 21 В. +ci 12 1 -2 3 1 -8 10 C. + C1 -1 1 -6 -8 -6 10 D. + Ci -6 -6 1 1 -1 10 Е. + ci -6 1 1arrow_forward
- . Give an example of a (nonzero) vector perpendicular to ?⃗ = ⟨−17, 3, −6⟩. Please give full explanation to the answerarrow_forward1. Determine "k" so that the vectors 3a- 4b and 5 a+ 2k b are collinear. Justify your response.arrow_forward-1 Let a = -2 and b = 1 be two vectors. -1, What is |a2 b|2- la - b|² ?arrow_forward
- a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =arrow_forwardLet a = (8,-6,7) and b = (-1,4, –3) be vectors. Compute the following (the answers to A, B, C are vectors and the answer to D is a number). A. a + b =D B. 8.a= C. a - b= D. a| = %3Darrow_forward6. Explain in words how a student would determine the magnitude of the vector P[2, 3, 1]. There is no need to solve the problem. You will be marked on how well you communicate your ideas. (arrow_forward
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